Method of and Apparatus for Evaluating the Performance of a Control System

ABSTRACT

A method of evaluating the performance of a control system using a computerized device includes calculating a ratio of a first area and a second area associated with a peak value of a signal associated with the control system, comparing the ratio with a predetermined value for the ratio, determining a cause of oscillation in the control system based on the comparison of the ratio with the predetermined value for the ratio, and providing a diagnosis of the cause of oscillation in the control system.

CROSS-REFERENCE TO RELATED PATENT APPLICATIONS

This application is a continuation-in-part of U.S. application Ser. No. 10/876,854, filed Jun. 25, 2005 and entitled “Method of and Apparatus for evaluating the performance of a control system,” the entire contents of which are hereby incorporated by reference.

BACKGROUND

The present description relates generally to methods of and apparatuses for evaluating the performance of a control system. More specifically, the present description relates to automated methods of and apparatuses for detecting and diagnosing oscillations in a feedback control loop.

Oscillating feedback control loops are a common occurrence in many types of control systems, such as heating, ventilating, and air conditioning (HVAC) systems. Oscillations are periodic changes that cause a signal within a feedback control loop to vary undesirably in a deterministic and repeatable fashion. Oscillating loops are undesirable because they increase variability in the quality of control and product performance, accelerate equipment wear, and may cause further oscillations in other interacting loops. Thus, detection, diagnosis, and correction of oscillations are important activities in feedback control loop supervision and maintenance.

Common causes of oscillations in feedback control loops include external oscillating disturbances, bad controller tuning, nonlinearities in a system component, such as static and dynamic nonlinearities, stiction (i.e., a sticking valve), incorrect component sizing, and poor actuator resolution, or a combination of these causes. Causes such as static and dynamic nonlinearities, stiction, incorrect component sizing, and poor actuator resolution are classified as system problems. External oscillating disturbances and bad controller tuning are classified as control problems.

Oscillation diagnosis involves distinguishing between these different causes of oscillations once they have been detected. Distinguishing between these types of causes is important for identifying appropriate remedial action. For example, attempts at re-tuning a controller will be unsuccessful or inefficient where a system problem is the cause of the oscillations rather than a control problem.

One problem with existing methods of detecting oscillations is that they require prior specification of an expected time parameter for the feedback control loop. Usually the information is required to configure a noise filter, or to set detection thresholds. This information is often unavailable or cannot be reliably estimated. Further, existing methods of diagnosing oscillations typically require a manual visual inspection of the shape of several different signals in the oscillating feedback control loop in order to distinguish between control problems and system problems. These requirements increase the required effort and costs associated with implementing the diagnosis method.

Thus, there is need for a method of and apparatus for evaluating the performance of a control system which does not require prior information about the feedback control loop being monitored. There is also need for an automated method of and apparatus for evaluating the performance of a control system that does not require manually monitoring shapes of multiple signals in the feedback control loop. There is further need for a method of and apparatus for evaluating the performance of a control system that is automated such that it does not require a manual visual inspection of a signal to distinguish among different causes of oscillations. There is yet further need for a method of and apparatus for evaluating the performance of a control system that is intuitive, easily implemented either directly or remotely, and requires minimal computational effort. There is yet further need for a method of and apparatus for evaluating the performance of a control system that is configured to address the effects of noise on the diagnosis while minimizing corruption to the monitored signal. There is yet further need for a method of and apparatus for evaluating the performance of a control system that is configured to address uncertainty in the diagnosis so that different feedback control loops may be compared.

SUMMARY

According to an exemplary embodiment, a method of evaluating the performance of a control system using a computerized device includes calculating a ratio of a first area and a second area associated with a peak value of a signal associated with the control system, comparing the ratio with a predetermined value for the ratio, determining a cause of oscillation in the control system based on the comparison of the ratio with the predetermined value for the ratio, and providing a diagnosis of the cause of oscillation in the control system.

According to another exemplary embodiment, an apparatus for evaluating the performance of a control system includes a processor operable to execute a diagnostic function, wherein the diagnostic function is configured to perform the steps of calculating a ratio of a first area and a second area associated with a peak value of a signal associated with the control system, comparing the ratio with a predetermined value for the ratio, determining a cause of oscillation in the control system based on the comparison of the ratio with the predetermined value for the ratio, and providing a diagnosis of the cause of oscillation in the control system.

Other features and advantages of the present invention will become apparent to those skilled in the art from the following detailed description and accompanying drawings. It should be understood, however, that the detailed description and specific examples, while indicating preferred embodiments of the present invention, are given by way of illustration and not limitation. Many modifications and changes within the scope of the present invention may be made without departing from the spirit thereof, and the invention includes all such modifications.

BRIEF DESCRIPTION OF THE DRAWINGS

The exemplary embodiments will hereafter be described with reference to the accompanying drawings, wherein like numerals depict like elements, and:

FIG. 1 is a diagram which illustrates an apparatus for evaluating the performance of a control system according to an exemplary embodiment;

FIG. 2 is a diagram which illustrates an exemplary feedback control loop which may be tested using the apparatus of FIG. 1;

FIG. 3 is a flow diagram which illustrates a method of detecting oscillations according to an exemplary embodiment;

FIG. 4 graphically illustrates exemplary areas before and after peaks in an error signal for oscillations caused by system problems, and in an error signal for oscillations caused by control problems;

FIG. 5 is a flow diagram which illustrates a method of distinguishing between oscillations caused by control problems and oscillations caused by system problems according to an exemplary embodiment; and

FIG. 6 is a flow diagram which illustrates a method of addressing the effects of noise on a diagnosis of a cause of oscillations in a control system according to an exemplary embodiment.

DETAILED DESCRIPTION

In the following description, for the purposes of explanation, numerous details are set forth in order to provide a thorough understanding of the present invention. It will be evident to one skilled in the art, however, that the exemplary embodiments may be practiced without these specific details. In other instances, structures and device are shown in diagram form in order to facilitate description of the exemplary embodiments. Furthermore, while the exemplary embodiments are often described in the context of an HVAC control system utilizing proportional plus integral (PI) action controllers, it should be understood that the disclosed method of and apparatus for evaluating the performance of a control system may be used in any of a variety of control systems and control methodologies.

FIG. 1 illustrates a testing tool 100 for evaluating the performance of a control system 110 according to an exemplary embodiment. Testing tool 100 includes an oscillation detection function 120 and an oscillation diagnosis function 130. While testing tool 100 is illustrated in FIG. 1 as including both oscillation detection function 120 and oscillation diagnosis function 130, it should be understood that many other configurations are possible. For example, according to other embodiments, testing tool 100 optionally excludes either oscillation detection function 120 or oscillation diagnosis function 130. According to yet other embodiments, oscillation detection function 120 and oscillation diagnosis function 130 are combined as a single function. Testing tool 100 may generally be used to evaluate the performance of control system 110. More specifically, testing tool 100 may be used to detect and diagnose oscillations in a control loop, such as a control loop in an HVAC system.

Testing tool 100 may be implemented as any general purpose computing device, such as a microprocessor device with sufficient memory and processing capability. An exemplary device may include a general purpose computing device in the form of a conventional computer, including a processing unit, a system memory, and a system bus that couples various system components including the system memory to the processing unit. The system memory may include read only memory (ROM) and random access memory (RAM). The computer may also include a magnetic hard disk drive for reading from and writing to a magnetic hard disk, a magnetic disk drive for reading from or writing to a removable magnetic disk, and an optical disk drive for reading from or writing to removable optical disk such as a CD-ROM or other optical media. The drives and their associated computer-readable media provide nonvolatile storage of computer-executable instructions, data structures, program modules and other data for the computer. Testing tool 100 may be implemented on, for example, a desktop or other computer (e.g., a stand-alone system or a networked system of computers), or on a portable device (e.g., laptop computer, personal digital assistant (PDA), etc.). For example, in the illustrated embodiment, testing tool 100 is implemented on a laptop computer which may be made available to field service personnel. According to another exemplary embodiment, testing tool 100 is integrated into a device, such as a controller, within control system 110.

Testing tool 100, in some embodiments, may be operated in a networked environment using logical connections to one or more remote computers having processors. Logical connections may include a local area network (LAN) and a wide area network (WAN) that are presented here by way of example and not limitation. Such networking environments are commonplace in office-wide or enterprise-wide computer networks, intranets and the Internet. Those skilled in the art will appreciate that such network computing environments will typically encompass many types of computer system configurations, including personal computers, hand-held devices, multi-processor systems, microprocessor-based or programmable consumer electronics, network PCs, minicomputers, mainframe computers, and the like. Testing tool 100 may also be implemented in distributed computing environments where tasks are performed by local and remote processing devices that are linked (either by hardwired links, wireless links, or by a combination of hardwired or wireless links) through a communications network. In a distributed computing environment, program modules may be located in both local and remote memory storage devices.

Testing tool 100, in other embodiments, may be implemented as software or a web application. Software and web implementations may be accomplished with standard programming techniques with rule based logic and other logic to accomplish the various database searching steps, correlation steps, comparison steps and decision steps. It should also be noted that software and web implementations may include implementations using one or more lines of software code, and/or hardware implementations, and/or equipment for receiving manual inputs.

Testing tool 100 is configured to be coupled (e.g., communicatively coupled) to control system 110 such that data may be exchanged (e.g., control signal data, etc.) between testing tool 100 and control system 110. Such coupling may be direct or remote. For example, according to an exemplary embodiment, testing tool 100 is remotely coupled to control system 110 via an external network connection (e.g., internet, intranet, Ethernet, etc.) or the like. According to another embodiment, testing tool 100 is directly coupled to control system 110 via a suitable connection port or terminal on a controller or device within control system 110. Testing tool 100 may be coupled to control system 110 using any suitable connection type or method, such as a wireless connection, a detachable communication cable, a “hard-wired” or other electrical or electronic connection, and the like.

Control system 110 may be a system, such as an HVAC system, that may include one or more industrial controllers utilizing any of a variety of control methodologies. For example, in one embodiment the control methodology may be a proportional plus integral (PI) methodology, and control system 110 may include one or more digital PI controllers operating in discrete time which implement one or more feedback control loops. In other embodiments, control system 110 may include other types of control systems, methodologies, and control algorithms.

FIG. 2 illustrates an exemplary feedback control loop 200 in control system 110 (shown for reference) which may be tested using testing tool 100. Feedback control loop 200 includes a controller 202 and a plant 204, wherein plant 204 represents a device or system to be controlled by feedback control loop 200. In FIG. 2, s denotes the Laplace operator, G_(c)(s) is the transfer function for the controller and G_(p)(s) is the plant transfer function. R(s) is the input command or setpoint signal, Y(s) is the feedback signal which represents the variable being controlled, and E(s) is the error signal, which represents the difference between input command or setpoint signal R(s) and feedback signal Y(s). U(s) is the controller output, L(s) is a disturbance signal acting at the plant input, and V(s) is a disturbance signal acting on plant output. Preferably, feedback control loop 200 is designed so that error signal E(s) reaches zero at steady state. According to an exemplary embodiment, feedback control loop is a PI feedback control loop and the controller transfer function is given by: $\begin{matrix} {{G_{c}(s)} = {\frac{U(s)}{E(s)} = {K_{c}\left( {1 + \frac{1}{T_{i\quad}s}} \right)}}} & (1) \end{matrix}$ where K_(c) is the controller gain and T_(i) is the integral time.

Referring again to FIG. 1, oscillation detection function 120 is configured to detect the presence of oscillations in control system 110, such as oscillations within feedback control loop 200 shown in FIG. 2. Oscillations are periodic changes that cause a signal within feedback control loop 200 to vary in a deterministic and repeatable fashion. According to an exemplary embodiment, oscillation detection function 120 is configured to detect oscillations in feedback control loop 200 by detecting repeating patterns in error signal E(s). Error signal E(s) is acquired from feedback control loop 200 by, for example, directly measuring the difference between input command or setpoint signal R(s) and feedback signal Y(s), by estimating E(s) from another signal in feedback control loop 200, etc.

According to an exemplary embodiment, oscillation detection function 120 is configured to use autocorrelation information as a way to characterize properties of error signal E(s). The properties of error signal E(s) are then converted to system properties and an index is calculated that describes the stochastic control performance of feedback control loop 200. The index is preferably normalized between zero and one. Other exemplary oscillation detection functions are described in detail in co-pending U.S. application Ser. No. 10/844,663, filed May 13, 2004 entitled “Method of and System for Evaluating the Performance of a Control System,” the entire contents of which are incorporated herein by reference.

FIG. 3 illustrates a method 300 of detecting oscillations using a normalized index according to an exemplary embodiment. The method begins with a step 310. In step 310 the lag-one autocorrelation is determined from sample measurements (e.g., discrete, or digital samples) of error signal E(s) acquired from control system 110. The lag-one autocorrelation is determined from zero crossing information in the samples of error signal E(s) using the exemplary cosine formula: {circumflex over (ρ)}_(e,1)=cos(π{tilde over (D)} ₁)  (2) where {tilde over (D)}₁ is the average number of zero-crossings per sample of error signal E(s).

In a step 320, error signal E(s) is filtered using a first order filter that is parameterized with the lag-one autocorrelation from step 310. An exemplary first order filter is given by: $\begin{matrix} {{H\left( q^{- 1} \right)} = \frac{1}{1 - {{\hat{\rho}}_{e,1}q^{- 1}}}} & (3) \end{matrix}$ The filtered error signal is denoted by e_(f,t), where e_(f,t)=H(q⁻¹)e_(t). The effect of the filtering operation is to add a new pole to the original process.

In a step 330, filtered error signal e_(f,t) is modeled as a second-order autoregressive moving average (ARMA (2,1)) process, and the coefficients in the denominator (1+w₁q⁻¹+w₂q⁻²) of the ARMA (2,1) model are estimated from the measurements of filtered error signal e_(f,t). The coefficients may be estimated by solving the following two exemplary simultaneous equations: $\begin{matrix} {w_{1} = \frac{{{\hat{\rho}}_{1}{\hat{\rho}}_{2\quad}} - {\hat{\rho}}_{3}}{{\hat{\rho}}_{2} - {\hat{\rho}}_{1}^{2}}} & (4) \\ {w_{2} = \frac{{{\hat{\rho}}_{1}{\hat{\rho}}_{3}} - {\hat{\rho}}_{2}^{2}}{{\hat{\rho}}_{2} - {\hat{\rho}}_{1}^{2}}} & (5) \end{matrix}$

In Eqs. (4) and (5), the autocorrelation lags {circumflex over (ρ)}₁, . . . {circumflex over (ρ)}₃ can be estimated from a set of higher-order crossings using the following exemplary formulae: {circumflex over (ρ)}₁=cos(π{tilde over (D)} ₁) {circumflex over (ρ)}₂=−(2−2{circumflex over (ρ)}₁)cos(π{tilde over (D)} ₂)+(−1+2{circumflex over (ρ)}₁) {circumflex over (ρ)}₃=(6−8{circumflex over (ρ)}₁+2{circumflex over (ρ)}₂)cos(π{tilde over (D)} ₃)−(−4+7{circumflex over (ρ)}₁−4{circumflex over (ρ)}₂)  (6) where {tilde over (D)}₁, {tilde over (D)}₂, {tilde over (D)}₃ are the first three higher-order crossings counts per sample in filtered error signal e_(f,t). The set of higher-order crossings is obtained by counting crossing events in repeatedly differenced versions of filtered error signal e_(f,t). For example, {tilde over (D)}₂ would be obtained by counting the number of zero crossings in the first difference of filtered error signal e_(f,t) and dividing by the number of samples minus one.

In a step 340, the damping ratio ζ of the second-order characteristic equation for the ARMA (2,1) model obtained in step 330 is calculated and this damping ratio ζ is used as a control performance index η. To calculate damping ratio ζ, the second-order characteristic equation is first transformed into the z-domain according to the following exemplary equation: 1+w ₁ q ⁻¹ +w ₂ q ⁻² W _(q)(z)=(z−r ₁)(z−r ₂)  (7) where the roots r₁ and r₂ are obtained by solving the following quadratic equations: $\begin{matrix} {{r_{1} = {\frac{1}{2}\left( {{- w_{1}} + \sqrt{w_{1}^{2} - {4w_{2}}}} \right)}},{r_{2} = {\frac{1}{2}\left( {{- w_{1}} - \sqrt{w_{1}^{2} - {4w_{2}}}} \right)}}} & (8) \end{matrix}$

Given that poles at s=p in the s-plane map onto poles at z=e^(pΔt) in the z-plane, expressions for damping ratio ζ and natural frequency ω_(n) of the second-order characteristic equation are derived from the phase and magnitude of W_(q)(z) for the case when the roots are complex conjugates as given by: $\begin{matrix} {\phi = {\Delta\quad t\quad\omega_{n}\sqrt{\left( {1 - \zeta^{2\quad}} \right)}}} & (9) \\ {M = {{\exp\left( {{- \Delta}\quad t\quad{\zeta\omega}_{n}} \right)} = {\exp\left( \frac{- {\phi\zeta}}{\sqrt{\left( {1 - \zeta^{2}} \right)}} \right)}}} & (10) \end{matrix}$ where $\phi = {{{\angle W}_{q}(z)} = {\tan^{- 1}\left( {\frac{- 1}{w_{1\quad}}\sqrt{\left| {w_{1}^{2} - {4w_{2}}} \right|}} \right)}}$ is the phase and $M = {\left. ||{W_{q}(z)} \right.|| = {\frac{1}{2}\sqrt{\left. {w_{1}^{2} +} \middle| {w_{1}^{2} - {4w_{2}}} \right|}}}$ is the magnitude of the complex conjugate roots, and Δt is the sample period.

Eqs (9) and (10) can be rearranged to provide the following expression for damping ratio ζ and thus control performance index η: $\begin{matrix} {\eta = \frac{{\pm \ln}\quad(M)}{\sqrt{{\ln^{2}(M)} + \phi^{2}}}} & (11) \end{matrix}$ where control performance index η is set to the positive root value. Real z-plane roots map onto real roots in the s-plane roots. Damping ratio ζ and thus control performance index η of the second-order characteristic equation with two real roots can be calculated from: $\begin{matrix} {\eta = {- {\frac{1}{2}\left\lbrack \frac{{\ln\left( r_{1} \right)} + {\ln\left( r_{2} \right)}}{\sqrt{{\ln\left( r_{1} \right)}{\ln\left( r_{2} \right)}}} \right\rbrack}}} & (12) \end{matrix}$

Control performance index η will be close to zero when error signal E(s) is oscillating. Oscillations are detected by checking when control performance index η violates a threshold. For example, according to an exemplary embodiment, error signal E(s) is oscillating when η<δ, where δ is a small number such as 0.1.

Thus, the method of and apparatus for evaluating the performance of a control system is configured to detect and diagnose oscillations without requiring any prior information about the feedback control loop being monitored, which facilitates easy implementation. Further, because the method and apparatus is capable of detecting and diagnosing oscillations based on a single signal from feedback control loop 200, it is applicable to a broad range of control systems, such as those with staged control, and also reduces the effort and cost required for implementation. The method of and apparatus for evaluating the performance of a control system also provides an intuitive index for detecting oscillations which is computationally simple and robust.

Referring again to FIG. 1, oscillation diagnosis function 130 is configured to diagnose the cause of oscillations present in control system 110, such as oscillations detected within feedback control loop 200 shown in FIG. 2 using, for example, oscillation detection function 120. More specifically, oscillation diagnosis function 130 is configured to distinguish between oscillations within feedback control loop 200 which are the result of control problems and oscillations within feedback control loop 200 which are the result of system problems. Control problems include such causes of oscillations as external oscillating disturbances to feedback control loop 200 and inadequate controller tuning (e.g., aggressive controller tuning) within feedback control loop 200. System problems include such causes of oscillations as static and dynamic nonlinearities of a device, a sticking valve, or insufficient valve actuator resolution in feedback control loop 200.

Oscillation diagnosis function 130 is configured to distinguish between oscillations caused by control problems and oscillations caused by system problems based on sample measurements of error signal E(s) in feedback control loop 200. Preferably, error signal E(s) is sampled at a rate sufficiently fast to capture key features of error signal E(s), such as curvatures, peaks, and zero crossings. It is also preferable to reduce the effects of noise. This may be accomplished by, for example filtering error signal E(s) using a low-pass filter, or by using the method described below for addressing the effects of noise.

According to an exemplary embodiment, oscillation diagnosis function 130 is configured to distinguish between oscillations caused by control problems and oscillations caused by system problems by calculating the ratio of areas between zero crossings before and after a peak in error signal E(s). To illustrate, FIG. 4 graphically illustrates exemplary areas before and after peaks in an error signal E(s) 410 for oscillations caused by system problems, and in an error signal E(s) 420 for oscillations caused by control problems. For oscillations caused by system problems, such as a sticking valve, error signal E(s) 410 is typically characterized by a shape having an exponential rise and decay. This exponential rise and decay is detected by calculating two areas associated with a half-cycle of a graphical representation of error signal E(s), and then calculating the ratio of the two areas to assess symmetry in error signal E(s). An area A₁ is defined between a zero crossing 412 and a peak 414 of error signal E(s), and an area A₂ is defined between peak 414 and a zero crossing 416. The ratio of A₁ and A₂ is given by: R=A ₁ /A ₂  (13)

As area A₁ is typically larger than area A₂ for error signal E(s) 410 for oscillations caused by system problems, the ratio of R=A₁/A₂ is greater than one.

For oscillations caused by control problems, such as an aggressively tuned controller, the error signal E(s) 420 is typically sinusoidal in shape. This sinusoidal shape is similarly detected by calculating two areas associated with a half-cycle of a graphical representation of error signal E(s), and then calculating the ratio of the two areas to assess symmetry in, error signal E(s). An area A₁ is defined between a zero crossing 422 and peak 424 of error signal E(s) 420 and an area A₂ is defined between peak 424 and a zero crossing 426. As area A₁ is typically equal to area A₂ for error signal E(s) 420, the ratio of R=A₁/A₂ is approximately one.

In order to distinguish between oscillations caused by control problems and oscillations caused by system problems, the ratio of R=A₁/A₂ is compared with a value of 1+δ, where δ is a tunable threshold value that determines the sensitivity of oscillation diagnosis function 130, and may be set to the desired value. Selecting a small value of δ results in high sensitivity and a larger probability of a false diagnosis, while selecting a larger value of δ results in reduced sensitivity and a smaller probability of a false diagnosis. According to an exemplary embodiment, a value of δ=1 is used. It should be understood that δ as used in oscillation diagnosis function 130 is different from and independent of δ as used in oscillation detection function 120, and that the two values are not necessarily the same.

FIG. 5 illustrates a method 500 of distinguishing between oscillations caused by control problems and oscillations caused by system problems according to an exemplary embodiment. The method begins with a step 510. In step 510, sampling data for error signal E(s) is acquired for a feedback control loop in which oscillations have been detected. According to an exemplary embodiment, the oscillations are detected using oscillation detection function 120, and the samples of error signal E(s) are filtered using a digital low-pass filter having a coefficient selected as a function of the lag-one correlation function determined by oscillation detection function 120.

In a step 520, Eq. (13) is used to calculate a ratio R of two areas associated with error signal E(s) as described above with reference to FIG. 4. In a step 530, the calculated value of ratio R is compared with a quantity 1+δ, where δ is a threshold that determines the sensitivity of the diagnosis as described above. If the calculated value of R is equal to or greater than 1+δ, then a system problem, such as a sticking valve, is diagnosed as the cause of the oscillations in a step 540. If the calculated value of R is less than 1+δ then a control problem, such as an aggressively tuned controller or an external disturbance, is diagnosed as the cause of the oscillations in a step 540.

The method of and system for evaluating the performance of a control system may be configured to address the effects of noise present in error signal E(s) on the diagnosis of the oscillation behavior under investigation. Noise present in error signal E(s) at certain frequencies may cause, for example, additional zero-crossings that do not relate to the oscillation behavior under investigation. Accordingly, a value of ratio R calculated for a peak in error signal E(s) associated with a zero-crossing caused by noise may not be effective in diagnosing the oscillation behavior under investigation.

According to an exemplary embodiment, noise filtering based on a frequency specification may be performed by operating directly on the values of ratio R. Operating directly on the values of ratio R may avoid corruption of error signal E(s) that may be caused by other noise filtering methods, such as filtering error signal E(s) in the time domain. The values of ratio R represent features of error signal E(s) captured at certain frequencies, as determined by the period T/2 between zero-crossings before and after a peak in error signal E(s). The notation “T/2” is used to indicate that the period between these zero crossings is a half-cycle of error signal E(s). Each value of ratio R may be related to the frequency at which it was extracted based on the period T/2 between these zero-crossings. Values of ratio R associated with certain frequencies may be eliminated or retained from a set of values of ratio R by examining the period T/2 between zero-crossings before and after the peak in error signal E(s) associated with each value of ratio R. For example, the period T/2 associated with each value of ratio R may be compared to a threshold value in order to determine which values of ratio R are to be retained for use in the diagnosis, and which are to be eliminated. The threshold value may be selected so that, for example, values of ratio R having a period T/2 corresponding to particular noise frequencies above or below a desired cut-off frequency are eliminated from the diagnosis.

FIG. 6 illustrates a method 600 of addressing the effects of noise on a diagnosis of a cause of oscillations in a control system according to an exemplary embodiment. The method begins with a step 610. In step 610, a signal feature to potentially be used to determine a cause of oscillation in the control system is calculated from signal information for a signal associated with the control system (e.g., error signal E(s) or another signal). The signal information includes, for example, samples of the signal that may capture features such as the peak value of the signal, zero crossings before and after the peak value of the signal, the period T/2 between zero-crossings before and after the peak value of the signal, areas between the peak value and the zero crossings, a value of ratio R, etc. According to an exemplary embodiment, a value of ratio R is calculated in step 610.

In a step 620, a signal feature to be used for purposes of noise filtering is calculated from the signal information. This signal feature may be the same or a similar feature as the signal feature calculated in step 610, or may be a different feature. For example, the signal feature calculated in step 610 may be a value of ratio R, while the signal feature calculated in step 620 is an area used to calculate the value of ratio R. According to an exemplary embodiment, the signal feature calculated in step 610 is a value of ratio R, and the signal feature calculated in step 620 is the period T/2 between zero-crossings before and after the peak in error signal E(s) associated with the value of ratio R.

In a step 630, the signal feature to be used for purposes of noise filtering calculated in step 620 is compared with a threshold value. According to an exemplary embodiment, the period T/2 is compared with a threshold value based on a period of oscillation T_(osc) of the signal. T_(osc) provides an estimate of the overall cycle period of the signal, whereas the period T/2 is the period of a particular half-cycle of the signal between zero-crossings before and after a particular peak value of the signal. T_(osc) may be determined for the signal using a standard method, such as a Fast Fourier Transform (FFT) or other suitable method.

The threshold value is selected to implement a desired cut-off frequency. The cut-off frequency is selected to eliminate or retain values of the feature calculated in step 610 that are associated with certain frequencies, such as possible noise frequencies. According to an exemplary embodiment, the cut-off frequency is selected to be approximately three times the frequency of oscillation f_(osc) of the signal, where 3f_(osc)=3/T_(osc). To implement this cut-off frequency, the value based on the period of oscillation T_(osc) of the signal is selected to be (T_(osc)/3)/(2)=T_(osc)/6, which facilitates comparison with the period T/2 for a particular half-cycle of the signal.

Depending on the result of the comparison in step 630, the signal feature determined in step 610 is either used to determine a cause of oscillation in the control system in a step 640 or is eliminated in a step 650. According to an exemplary embodiment, if a period T/2 calculated in step 620 is equal to or greater than a value based on the period of oscillation T_(osc) of the signal, a value of ratio R determined in step 610 is retained and used to determine a cause of oscillation in the control system in step 640. If the period T/2 is less than the value based on the period of oscillation T_(osc) of the signal, the value of ratio R determined in step 610 is eliminated in step 650, and is not used to determine the cause of oscillation in the control system. In a step 660, the result of the diagnosis may be provided as an output. For example, the result of the diagnosis may be presented to a user (e.g., via a display, a printed report, etc.) or provided as an input to another diagnostic function or system.

The method of and system for evaluating the performance of a control system may be configured to address uncertainty in a set of values of ratio R. Uncertainty in a set of values of ratio R may be caused by, for example, changes in characteristics of the control system, static and dynamic non-linearities in the control system, or the particular vulnerability of the location of a peak in error signal E(s) to noise and other disturbances. The method of and system for evaluating the performance of a control system may be configured to address this uncertainty by providing the result of the diagnosis in the form of a probability that a particular cause of oscillation exists.

According to an exemplary embodiment, uncertainty in a set of values of ratio R may be accounted for by calculating a probability of a value of ratio R being larger than a predetermined value. According to an exemplary embodiment, a value of 1 is used. If the calculated probability is large, then a system problem, such as a sticking valve, is diagnosed as the cause of the oscillations. If the calculated probability is small, then a control problem, such as an aggressively tuned controller or an external disturbance, is diagnosed as the cause of the oscillations.

The values of ratio R for a considered control loop may be converted into a probability measure by calculating a t-statistic. If the values of ratio R are not Normally distributed, a transformation, such as, for example, a logarithmic or power transformation, may be applied to obtain Normally distributed values. A t-statistic is given by: $\begin{matrix} {t_{\overset{\_}{R}\quad} = \frac{\overset{\_}{R} - \xi}{{\overset{\sim}{s}}_{\overset{\_}{R}}}} & (14) \end{matrix}$ where R is the sample mean, ξ is the predetermined value, and {tilde over (S)} _(R) is the estimated standard-error of the population mean given by: $\begin{matrix} {{\overset{\sim}{s}}_{\overset{\_}{R}} = \frac{{\overset{\sim}{s}}_{R}}{\sqrt{N_{\overset{\_}{R}}}}} & (15) \end{matrix}$ where {tilde over (s)}_(R) is the sample standard deviation and N _(R) is the number of samples. The probability of the sample mean being greater than the threshold is given by: $\begin{matrix} {P_{S} = {\int_{- \infty}^{\overset{\_}{R}}{{t_{v}(z)}\quad{\mathbb{d}z}}}} & (16) \end{matrix}$ where t_(v)(z) is the Student's t probability density function with v=N_(R)−1 degrees of freedom. The quantity P_(s) represents a measure of the probability that stiction is present. P_(s) is naturally normalized so that the performance of different control loops may be compared in a way that accounts for uncertainty in a set of values of ratio R.

Thus, the method of and system for evaluating the performance of a control system is capable of diagnosing oscillations using a minimal number of signals from a feedback control loop, which reduces the required effort and cost of implementation. The method and apparatus also simplifies diagnosis by providing an automated way to distinguish among different causes of oscillations that utilizes the calculation of a ratio of areas associated with a single control signal, and that does not require a manual visual inspection of various control signal waveforms. The method of and apparatus for evaluating the performance of a control system also provides a technique for distinguishing between possible causes of oscillations which is computationally simple and robust. The method of and apparatus for evaluating the performance of a control system is also easily implemented either directly or remotely, such that the proper diagnosis may be made before deciding whether it is necessary to dispatch service personnel to a remote site. The method of and apparatus for evaluating the performance of a control system may be configured to address the effects of noise on the diagnosis while minimizing corruption to the monitored signal, and may be configured to address uncertainty in the diagnosis so that different feedback control loops may be compared.

It should be understood that the construction and arrangement of the elements of the exemplary embodiments are illustrative only. Although only a few embodiments of the present invention have been described in detail in this disclosure, many modifications are possible without materially departing from the novel teachings and advantages of the subject matter recited in the claims. Accordingly, all such modifications are intended to be included within the scope of the present invention as defined in the appended claims. Unless specifically otherwise noted, the claims reciting a single particular element also encompass a plurality of such particular elements. The order or sequence of any process or method steps may be varied or re-sequenced according to alternative embodiments. In the claims, any means-plus-function clause is intended to cover the structures described herein as performing the recited function and not only structural equivalents but also equivalent structures. Other substitutions, modifications, changes and/or omissions may be made in the design, operating conditions and arrangement of the exemplary embodiments without departing from the spirit of the present invention as expressed in the appended claims. 

1. A method of evaluating the performance of a control system using a computerized device, the method comprising: calculating a ratio of a first area and a second area associated with a peak value of a signal associated with the control system; comparing the ratio with a predetermined value for the ratio; determining a cause of oscillation in the control system based on the comparison of the ratio with the predetermined value for the ratio; and providing a diagnosis of the cause of oscillation in the control system.
 2. The method of claim 1, wherein determining the cause of the oscillation in the control system includes distinguishing between a first cause and a second cause by selecting the first cause if the ratio is greater than or equal to the predetermined value for the ratio and selecting the second cause, and selecting the second cause if the ratio is less than the predetermined value for the ratio.
 3. The method of claim 2, wherein one of the first cause and the second cause is a system problem and the other of the first cause and the second cause is a control problem.
 4. The method of claim 1, wherein the ratio is a first feature of the signal, and wherein the method further comprises: calculating a second feature of the signal; comparing the second feature with a predetermined value for the second feature; and performing one of using the ratio to determine the cause of oscillation and not using the ratio to determine the cause of oscillation in the control system based on the comparison of the second feature with the predetermined value for the second feature.
 5. The method of claim 4, wherein the second feature is a first period associated with the peak value of the signal, and wherein the predetermined value for the second feature is a value based on a second period of the signal.
 6. The method of claim 1, further comprising detecting an oscillation in the control system.
 7. The method of claim 6, wherein detecting the oscillation in the control system comprises calculating a performance index value for the control system based on the signal.
 8. The method of claim 1, further comprising determining a probability of the cause of oscillation.
 9. The method of claim 1, wherein the signal is a controller error signal.
 10. The method of claim 1, wherein the control system is a heating, ventilating, and air conditioning system.
 11. An apparatus for evaluating the performance of a control system, the apparatus comprising: a processor operable to execute a diagnostic function, wherein the diagnostic function is configured to perform the steps of: calculating a ratio of a first area and a second area associated with a peak value of a signal associated with the control system; comparing the ratio with a predetermined value for the ratio; determining a cause of oscillation in the control system based on the comparison of the ratio with the predetermined value for the ratio; and providing a diagnosis of the cause of oscillation in the control system.
 12. The apparatus of claim 11, wherein determining the cause of the oscillation in the control system includes distinguishing between a first cause and a second cause by selecting the first cause if the ratio is greater than or equal to the predetermined value for the ratio and selecting the second cause, and selecting the second cause if the ratio is less than the predetermined value for the ratio.
 13. The apparatus of claim 12, wherein one of the first cause and the second cause is a system problem and the other of the first cause and the second cause is a control problem.
 14. The apparatus of claim 11, wherein the ratio is a first feature of the signal, and wherein the diagnostic function is further configured to perform the steps of: calculating a second feature of the signal; comparing the second feature with a predetermined value for the second feature; and performing one of using the ratio to determine the cause of oscillation and not using the ratio to determine the cause of oscillation in the control system based on the comparison of the second feature with the predetermined value for the second feature.
 15. The apparatus of claim 14, wherein the second feature is a first period associated with the peak value of the signal, and wherein the predetermined value for the second feature is a value based on a second period of the signal.
 16. The apparatus of claim 11, wherein the processor is further operable to execute a detection function configured to perform the step of detecting an oscillation in the control system.
 17. The apparatus of claim 16, wherein detecting the oscillation in the control system comprises calculating a performance index value for the control system based on the signal.
 18. The apparatus of claim 11, wherein the diagnostic function is further configured to perform the step of determining a probability of the cause of oscillation.
 19. The apparatus of claim 11, wherein the signal is a controller error signal.
 20. The apparatus of claim 11, wherein the control system is a heating, ventilating, and air conditioning system. 